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Proof step 92 from proof shiftright-rec-8-neg (previous step)

j0 * 256 >> (j - 1) = j0 >> (j - 9), 8 < j, abs(j1) < 2, j1 < j, j1 ≤ 0, j0 < 0, 0 < j, 512 * j0 + j1 < ~1, 512 * j0 + j1 < 0, ∀ i, j0. i→n(j0) < i→n(j) → 8 ≤ j0 ∧ i < 0 ∧ 0 < j0 ∧ 0 ≤ j0 → i >> j0 = (i - 255) / 256 >> (j0 - 8) ⊦ ((512 * j0 + j1) + 1) / 512 = 1 + j0, ((512 * j0 + j1) + 1) % 256 = 0, j = 8, j0 >> (j - 9) = (((512 * j0 + j1) + 1) / 512 - 1) >> (j - 9), j = 0

User applied rule cut formula

And obtained the following new goals

Proof step 93:
(512 * j0 + j1) + 1 = 512 * j0 + j1 + 1, j0 * 256 >> (j - 1) = j0 >> (j - 9), 8 < j, abs(j1) < 2, j1 < j, j1 ≤ 0, j0 < 0, 0 < j, 512 * j0 + j1 < ~1, 512 * j0 + j1 < 0, ∀ i, j0. i→n(j0) < i→n(j) → 8 ≤ j0 ∧ i < 0 ∧ 0 < j0 ∧ 0 ≤ j0 → i >> j0 = (i - 255) / 256 >> (j0 - 8) ⊦ ((512 * j0 + j1) + 1) / 512 = 1 + j0, ((512 * j0 + j1) + 1) % 256 = 0, j = 8, j0 >> (j - 9) = (((512 * j0 + j1) + 1) / 512 - 1) >> (j - 9), j = 0

Rule argument

fma: (512 * j0 + j1) + 1 = 512 * j0 + j1 + 1

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used formulas: (512 * j0 + j1) + 1 = 512 * j0 + j1 + 1